# For the Lagrangian of fermion masses, how do I understand?

• lhcQFT
In summary, the conversation is about fermion masses and the use of matrix notation in expressing terms related to SU(2) left-handed and right-handed lepton particles. The speaker is confused about how these terms can be gauge singlets and is requesting a detailed explanation.
lhcQFT
Hello, everyone.

I have a one question which is related to the fermion masses.
If you see my latex mathematics, you can know what I want to say.
Here, L means SU(2) left-handed lepton doublets and R means SU(2) right-handed lepton singlets.

So I am too much confusing to understand this mechanism. When I expanded lagrangian into components of lepton doublets and that of lepton singlets, I can't understand how these terms( (1x1) (2x2) (1x1) <= I expressed each term by using matrix notation ) can be gauge singlets? If you give me detailed explanation, I really thanks to you.

Have a good day.

what latex?

## 1. What is the Lagrangian of fermion masses?

The Lagrangian of fermion masses is a mathematical expression used in the Standard Model of particle physics to describe the behavior of fermions, which are fundamental particles with half-integer spin. It takes into account the mass of fermions and their interactions with other particles through the Higgs field.

## 2. How do I understand the Lagrangian of fermion masses?

Understanding the Lagrangian of fermion masses requires a strong background in quantum field theory and mathematical techniques such as group theory and gauge theory. It is a complex and abstract concept that is studied and applied by theoretical physicists to make predictions about the behavior of particles at the subatomic level.

## 3. What does the Lagrangian of fermion masses tell us about particles?

The Lagrangian of fermion masses provides information about the mass of fermions and how they interact with other particles. It also plays a crucial role in explaining the processes of particle creation and annihilation, as well as the behavior of particles in high-energy collisions.

## 4. How is the Lagrangian of fermion masses related to the Higgs mechanism?

The Lagrangian of fermion masses is closely tied to the Higgs mechanism, which is responsible for giving particles mass. The Higgs field interacts with fermions through the Lagrangian, resulting in the acquisition of mass by some particles and the remaining massless particles becoming the carriers of fundamental forces.

## 5. Why is the Lagrangian of fermion masses important in particle physics?

The Lagrangian of fermion masses is a fundamental component of the Standard Model of particle physics, which is the most successful theory to date in explaining the behavior of subatomic particles. It allows physicists to make predictions about the behavior of particles and their interactions, and has been confirmed by numerous experiments conducted at particle accelerators around the world.

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